In group theory, a word is any written product of group elements and their inverses. For example, if x, y and z are elements of a group G, then xy, z−1xzz...

word problem for groups; and the classical Burnside problem. See the book by Chandler and Magnus for a detailed history of combinatorial group theory...

the structure of a metric space, given by the so-called word metric. Geometric group theory, as a distinct area, is relatively new, and became a clearly...

In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely...

Word (computer architecture), a group of bits or digits/characters processed as a unit Word (formal language theory), a finite sequence of letters taken...

immediate precursor for small cancellation theory: this paper provided a solution of the word problem for a class of groups satisfying a complicated set of combinatorial...

geometry, in the sense of geometric group theory: one has the Cayley graph, which has a metric, called the word metric. These are also two resulting...

In group theory, a word metric on a discrete group G {\displaystyle G} is a way to measure distance between any two elements of G {\displaystyle G} ....

Scientific theories are the most reliable, rigorous, and comprehensive form of scientific knowledge, in contrast to more common uses of the word "theory" that...

the Sturm comparison theorem.: 114  Cutting sequence Word (group theory) Morphic word Lyndon word Hordijk, A.; Laan, D. A. (2001). "Bounds for Deterministic...

In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known...

of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group G {\displaystyle G} is the algorithmic problem...

words (followed by reduction if necessary) as group operation. The identity is the empty word. A reduced word is called cyclically reduced if its first and...

Word Processing in Groups is a monograph in mathematics on the theory of automatic groups, a type of abstract algebra whose operations are defined by...

Muted Group Theory (MGT) is a communication theory developed by cultural anthropologist Edwin Ardener and feminist scholar Shirley Ardener in 1975, that...

In mathematics, in the realm of group theory, a group is said to be thin if there is a finite upper bound on the girth of the Cayley graph induced by...

mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra:...

linguistics, these are known as phrasemes. In theories of syntax, a phrase is any group of words, or sometimes a single word, which plays a particular role within...

isotopy), and whose group operation is composition of braids (see § Introduction). Example applications of braid groups include knot theory, where any knot...

each other. In geometric group theory, a finitely generated group is viewed as a metric space using the word metric. If two groups are (abstractly) commensurable...

mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with...

representation theory (that is, through the representations of the group) and of computational group theory. A theory has been developed for finite groups, which...

prototypical example is the word problem for groups, but there are many other instances as well. Some deep results of computational theory concern the undecidablity...

In group theory, Matsumoto's theorem, proved by Hideya Matsumoto (1964), gives conditions for two reduced words of a Coxeter group to represent the same...

geometric group theory, the growth rate of a group with respect to a symmetric generating set describes how fast a group grows. Every element in the group can...

In the mathematical area of geometric group theory, a Van Kampen diagram (sometimes also called a Lyndon–Van Kampen diagram ) is a planar diagram used...

A word is a basic element of language that carries meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often...

roots of unity. In the theory of algebraic groups, a group element is unipotent if it acts unipotently in a certain natural group representation. A unipotent...

white extinction, or white replacement conspiracy theory is a white nationalist conspiracy theory that claims there is a deliberate plot (often blamed...

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called...